Learning mathematics through problem solving: Part 3

High-quality problem-based math curricula can make all the difference. With problem-based learning, teachers transfer the responsibility of the actual learning to students, offering support and scaffolding as students grasp both math concepts and math language. This mode of teaching aligns with the National Council for Teachers of Mathematics (NCTM) Effective Mathematics Teaching Practices.

By Amplify Staff | July 11, 2022

Tackling real-world questions as a path to math success

In previous posts, we’ve established that problem-based learning sets students up for long-term success. We’ve shown that problem-based lessons introduce students to interesting and often real-world problems or tasks, and described the key role teachers play in putting problem-based learning into action. 

In this post, we’ll look more closely at how teachers can support students engaging in problem-based learning, even when the students do much of their work together in groups. 

You can read the first post in this series here and the second post here

Teachers transfer learning responsibility to students

In a problem-based lesson, students are introduced to a handful of interesting and often real-world problems or tasks that can be worked out by referencing background knowledge, previously learned content, and newly provided information. 

With problem-based learning, teachers transfer the responsibility of the actual learning to students. Teachers set up the activities and lessons, then students are given the right information and scaffolds to make sense of math concepts and opportunities to practice and apply their learning. 

These problems are designed to get students thinking—and talking together—about solutions. This way, students begin to grapple with math content and grasp math language development.  

During class, the teacher’s role is to observe students, ask questions, select and share student work, and help students synthesize their learning at the end of the lesson. That’s where teachers help students apply new insights and conceptions to their bigger-picture understanding of the math at hand.

When students do need to be taught a process directly, teachers can shift from conceptual to procedural instruction. (For example, after making sense of adding signed rational numbers, students practice to gain fluency.) In these moments, the problem-based structure is focused more directly on producing answers and debugging procedures than on new sense-making.

Problem-based math teaching aligns with NCTM practices

The highest quality problem-based lessons embody all eight of the NCTM Teaching Practices. These are: 

  1. Establish mathematics goals to focus student learning.
  2. Implement tasks that promote reasoning and problem solving.
  1. Use and connect mathematical representations.
  2. Facilitate meaningful mathematical discourse.
  3. Pose purposeful questions.
  4. Build procedural fluency from conceptual understanding.
  5. Support productive struggle in learning mathematics.
  6. Elicit and use evidence of student thinking.

​​How Amplify Math can help teachers

We started with a world-class problem-based curriculum (Illustrative Mathematics’® IM K–12 Math™) and made changes to help educators implement engaging problem-based core curriculum for students. Amplify Math helps shift to planning and teaching problem-based lessons, tracking student progress, and differentiating instruction based on real-time data. We’ve made the math problems more exciting and relevant for all students, thus making it easier for all students to become active participants in their learning.

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